depending on the game it can be. if the game is cpu intensive you could be running into a slight drawback if any with your cpu but honestly i dont think it would be enough if any to upgrade to a better cpu with that gpu.
After a quick search, it looks like that CPU should have performance somewhat similar to the Athlon X4 760K, or a little weaker than the X4 860K or Pentium G3258. The 860K/G3258 are basically the entry level CPUs for a gaming rig. For a GTX 960, I think it's typically recommended to have an Intel i3, or AMD equivalent (probably an overclocked FX-6300), which would be more or less one tier up from your current CPU. So you may be bottlenecked a bit in some games.
Edit: check out Anand Bench for a rough estimate of bottlenecking: http://www.anandtech.com/bench/CPU/1288 http://www.anandtech.com/bench/CPU/1107
They have gaming benchmarks for CPUs paired with a GTX 770, which is fairly similar in performance to a GTX 960. They may not have benches for your CPU, but you can look at the scores for similar CPUs (e.g. a G3258, other A10-xxxx CPUs, etc) to give you a rough idea of where your CPU would fall. You can then compare to the scores for better CPUs to determine to what extent you're being bottlenecked.